Boiling and Condensation Heat Transfer

Why phase-change heat transfer matters

Almost every high-power thermal machine relies on boiling, condensation, or both, precisely because phase change moves so much heat across so small a temperature difference. A single-phase water loop might manage a convection coefficient of 500–2,000 W/m²K; put that same water into nucleate boiling and the coefficient jumps to tens of thousands — you can dump a megawatt per square metre while the wall sits only 20–30 °C above the saturation temperature.

• Steam power plants. Boiler tubes evaporate feedwater; the surface condenser condenses turbine exhaust steam, and its filmwise coefficient sets a large slice of the plant's thermal resistance.
• Nuclear reactors. Fuel-rod surfaces operate deep in nucleate boiling; staying safely below the departure-from-nucleate-boiling (DNB) point is a first-order safety constraint.
• Refrigeration and heat pumps. The evaporator boils refrigerant to absorb heat; the condenser rejects it by condensing.
• Electronics cooling. Immersion and two-phase cold plates exploit boiling to hold high-density chips near a fixed junction temperature.
• Heat pipes and thermosyphons. Sealed devices that boil at the hot end and condense at the cold end, moving heat with almost no temperature drop.
• Distillation and process reboilers. Chemical plants boil and condense to separate mixtures.
• Rocket engines. Regeneratively-cooled nozzles run the coolant near or into nucleate boiling to survive multi-MW/m² wall fluxes.

The boiling curve, step by step

The canonical picture is pool boiling: a heated horizontal surface submerged in an otherwise still pool of saturated liquid. Plot the surface heat flux q″ against the wall superheat ΔT_e = T_wall − T_sat, and you get the boiling curve, first mapped by Nukiyama in 1934. For water at 1 atm it has four distinct regimes:

1. Free convection (ΔT_e ≲ 5 °C). The wall is barely superheated; no bubbles form at the wall. Heat leaves by natural convection and single-phase liquid rises to the free surface to evaporate there. Coefficients are ordinary (hundreds of W/m²K).
2. Nucleate boiling (ΔT_e ≈ 5–30 °C). Vapor bubbles nucleate in microscopic surface cavities, grow, and detach. First isolated bubbles (point ONB, onset of nucleate boiling), then, as superheat rises, dense columns and vapor jets. Bubble departure pumps hot liquid away and drags cold liquid in, so the flux climbs steeply — q″ ∝ ΔT_e³ — to the peak. This is the useful regime: high flux at modest superheat.
3. Critical heat flux (the peak, q″_max). Near 1 MW/m² for water at 1 atm, so much vapor is generated that bubbles merge into an unstable film. Beyond this point, liquid can no longer freely rewet the surface. This is the burnout / DNB point — the most important number on the whole curve.
4. Transition boiling (ΔT_e ≈ 30–120 °C). A part-vapor, part-liquid regime where the surface oscillates between wetted and dry. Counter-intuitively the flux falls as superheat rises, because the growing vapor patches insulate the surface. The curve has a negative slope — an unstable region no heat-flux-controlled system can rest in.
5. Film boiling (ΔT_e ≳ 120 °C). A continuous, stable vapor film blankets the surface. Heat now crosses the film by conduction and radiation, so coefficients plummet and the wall must run very hot. The minimum of the curve (the Leidenfrost point) marks the transition into stable film boiling.

The subtlety is what you control. A heat-flux-controlled surface — an electric cartridge heater, a nuclear fuel rod — can only ride the ascending nucleate branch. Push it past q″_max and there is nowhere to go on the curve at that flux except deep in film boiling, so the wall temperature jumps by hundreds of degrees almost instantly. A temperature-controlled surface (condensing steam heating the wall from the far side) can traverse the whole curve, transition region included, without runaway.

Condensation: filmwise versus dropwise

Condensation is the mirror image — vapor gives up its latent heat at a subcooled surface — and it comes in two modes set almost entirely by surface wettability:

• Filmwise. The condensate wets the surface and forms a continuous liquid film that grows and drains under gravity. Heat must conduct through that film, and the film is the controlling resistance. Nusselt's 1916 laminar-film analysis gives the coefficient as a function of fluid properties, plate height, and temperature difference — typically 5,000–15,000 W/m²K for steam on a vertical plate.
• Dropwise. On a non-wetting surface the condensate beads into discrete droplets that grow, coalesce, and roll off, continually re-exposing bare metal to fresh vapor. Because the thin-film resistance is largely eliminated, coefficients leap 5–10×, into the 40,000–100,000+ W/m²K range.

Dropwise is the holy grail of condenser design, but it is notoriously hard to hold: the hydrophobic promoter coatings that induce it wear off, oxidize, or wash away over weeks to months, and the surface reverts to filmwise. For that reason virtually all industrial surface condensers are designed conservatively for filmwise condensation and treat any dropwise behavior as a bonus.

Governing equations and a worked example

The baseline definition is Newton's law of cooling with a phase-change coefficient:

q″ = h · ΔT_e    and    Q̇ = h · A · ΔT_e

where q″ is heat flux (W/m²), Q̇ total heat rate (W), h the boiling or condensation coefficient (W/m²K), A the surface area (m²), and ΔT_e = T_wall − T_sat the wall superheat (K, for boiling) — for condensation the driving difference is T_sat − T_wall.

For the nucleate-boiling branch itself, the standard tool is the Rohsenow correlation:

q″ = μ_l · h_fg · √[ g(ρ_l − ρ_v) / σ ] · [ c_p,l ΔT_e / (C_sf h_fg Pr_lⁿ) ]³

Symbols and units: μ_l liquid dynamic viscosity (Pa·s); h_fg latent heat of vaporization (J/kg); g gravity (9.81 m/s²); ρ_l, ρ_v liquid and vapor densities (kg/m³); σ surface tension (N/m); c_p,l liquid specific heat (J/kg·K); ΔT_e wall superheat (K); Pr_l liquid Prandtl number (–); n = 1 for water and 1.7 for other fluids; and C_sf the empirical surface–fluid constant (≈ 0.013 for water on polished copper, ≈ 0.006 for water on brass). The cubic dependence on ΔT_e is exactly why the nucleate branch is so steep.

The peak — the critical heat flux — has its own hydrodynamic prediction, the Zuber correlation:

q″_max = C · h_fg · ρ_v^1/2 · [ σ g (ρ_l − ρ_v) ]^1/4,   C ≈ 0.131 (Zuber constant)

Worked example — CHF of saturated water at 1 atm. Use h_fg = 2.257 × 10⁶ J/kg, ρ_v = 0.60 kg/m³, ρ_l = 958 kg/m³, σ = 0.0589 N/m, g = 9.81 m/s². Then:

[σ g (ρ_l − ρ_v)]^1/4 = [0.0589 × 9.81 × 957.4]^1/4 = (553)^1/4 ≈ 4.85

ρ_v^1/2 = 0.775

q″_max = 0.131 × 2.257×10⁶ × 0.775 × 4.85 ≈ 1.11 × 10⁶ W/m² ≈ 1.1 MW/m²

That matches the experimentally observed ~1 MW/m² CHF for water at atmospheric pressure — a reassuring cross-check, and a hard ceiling any water-cooled fuel rod or heater must respect with margin.

Regime comparison at a glance

Regime	Wall superheat ΔTe (water, 1 atm)	Mechanism	Typical h (W/m²K)
Free convection	< ~5 °C	Single-phase natural convection, surface evaporation	~100–1,000
Nucleate boiling	~5–30 °C	Bubbles nucleate, grow, depart; strong agitation	~5,000–100,000
Critical heat flux (peak)	~30 °C	Vapor merges into a film; q″max ≈ 1 MW/m²	peak of curve
Transition boiling	~30–120 °C	Unstable, part-film; flux falls with superheat	decreasing
Film boiling / Leidenfrost	> ~120 °C (≳200 °C surface)	Stable vapor blanket; conduction + radiation	~100–300
Filmwise condensation	—	Continuous draining liquid film (Nusselt)	~5,000–15,000
Dropwise condensation	—	Beading droplets roll off, re-expose surface	~40,000–100,000+

Common misconceptions and failure modes

• "More superheat always means more heat." False past the peak — in transition boiling, raising ΔT_e lowers the flux. The curve is non-monotonic.
• "Burnout means the fluid ran out." No — burnout (CHF/DNB) is the surface drying under a vapor film while fully submerged; it is a heat-transfer collapse, not a lack of liquid.
• "A hotter surface boils water faster." Above the Leidenfrost point a droplet actually survives longer, because the vapor cushion insulates it — the classic sizzling-drop demonstration.
• "Smooth polished surfaces boil best." The opposite — nucleation needs cavities. A too-smooth surface has few active sites, boils at higher superheat, and can suffer a large temperature overshoot at boiling incipience.
• "Condensers are limited by the steam side." In filmwise condensation the draining liquid film is usually the dominant resistance, not the vapor.
• "Non-condensable gas is harmless." A few percent of air in steam can slash the condensation coefficient by half or more, because gas accumulates at the interface and throttles vapor arrival — a real killer for power-plant condenser performance.
• "Design at the CHF." Never — heat-flux-controlled equipment is operated with a large CHF margin (a critical heat flux ratio, or DNBR, well above 1) precisely because crossing the peak is catastrophic and irreversible.